# Unmating of rational maps: Sufficient criteria and examples

# Unmating of rational maps: Sufficient criteria and examples

This chapter asks when a given (postcritically finite) rational map *f* arises as a mating. Mating occurs when the filled Julia sets of two polynomials of the same degree are dynamically related via external rays. This chapter seeks to tackle the opposite of mating—nonmating. To do this, a sufficient condition when the given rational map *f* arises as a mating is given. If this condition is satisfied, the chapter presents a simple explicit algorithm to unmate the rational map. This means that *f* is decomposed into polynomials that, when mated, yield *f*. Several examples of unmatings are then presented.

*Keywords:*
mating, unmating, rational maps, external rays, decomposition, polynomials

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